Evolutionary stability on graphs |
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Authors: | Ohtsuki Hisashi Nowak Martin A |
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Institution: | a Program for Evolutionary Dynamics, Harvard University, Cambridge, MA 02138, USA b Department of Organismic and Evolutionary Biology, Harvard University, Cambridge, MA 02138, USA c Department of Mathematics, Harvard University, Cambridge, MA 02138, USA |
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Abstract: | Evolutionary stability is a fundamental concept in evolutionary game theory. A strategy is called an evolutionarily stable strategy (ESS), if its monomorphic population rejects the invasion of any other mutant strategy. Recent studies have revealed that population structure can considerably affect evolutionary dynamics. Here we derive the conditions of evolutionary stability for games on graphs. We obtain analytical conditions for regular graphs of degree k>2. Those theoretical predictions are compared with computer simulations for random regular graphs and for lattices. We study three different update rules: birth-death (BD), death-birth (DB), and imitation (IM) updating. Evolutionary stability on sparse graphs does not imply evolutionary stability in a well-mixed population, nor vice versa. We provide a geometrical interpretation of the ESS condition on graphs. |
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Keywords: | Evolutionary game theory Evolutionary graph theory ESS Structured population Spatial games |
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